Recurrent network - sequence prediction

Progress:

Specifies the numerical sequence for which you want to predict the n-e number of items. Also, the following parameters are specified:

• The size of the window
• The number of hidden layer elements
• The maximum permissible error
• N, the number of elements to predict
• number of iterations

Elman neural network has 3 matrix of weighting coefficients:

1. Between input neurons and hidden layer, then W
2. Between contextual neurons and hidden layer, then U
3. Between the hidden layer and output, then W1

The next step is to initialize the values ​​of the weights. Each weight is given a random value [-1, 1].

Result of work

The Fibonacci sequence

Network settings:

• Window size = 2;
• Neurons number = 4;
• Error = 0.0048;
• Step = 0.00001;
• Sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, 34), 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946
• The sample for the study: the first 10 numbers of the sequence;
• The number of iterations performed: 33412;

Периодическая последовательность

Параметры сети:

• Window size = 4;
• Neurons number = 8;
• Error = 0.0001;
• Step = 0.000001;
• Sequence: (15,-13,6,47,15,-13,6,47,15,-13,6,47), 15, -13, 6, 47, ...
• The sample for the study: the first 12 numbers of the sequence;
• The number of iterations performed: 56599;

Факториал

Параметры сети:

• Window size = 3;
• Neurons number = 6;
• Error = 0.05;
• Step = 0.000001;
• Sequence: (1, 2, 6, 24, 120, 720, 5040), 40320, 362880, 3628800
• The sample for the study: the first 7 numbers of the sequence;
• The number of iterations performed: 56599;

Example